The similarity solutions using Lie group analysis for shock wave propagation in a rotational axisymmetric non-ideal gas with azimuthal or axial magnetic field in the case of isothermal and adiabatic flows are obtained. All possible cases of similarity solutions are discussed using the Lie group analysis for the isothermal and adiabatic flows. The arbitrary constants involved in the generators of local Lie groups bring various possible cases of solutions with exponential law and power law shock paths. Similarity solution for isothermal and adiabatic flows with power law shock path is discussed in detail. The density of ambient medium is taken to be constant. The axial and azimuthal fluid velocities and magnetic field in the ambient medium are assumed to be varying according to power law. The effect on shock wave strength and that on the flow variables due to variation of the Alfven Mach number, adiabatic index of the gas, non-idealness parameter, rotational parameter and initial magnetic field variation exponent are investigated. It is found that these parameters have decaying effects on shock wave. The obtained results in the case of isothermal and adiabatic flows are also compared with each other.

在等温流和绝热流的情况下，使用李群分析获得了在具有方位角或轴向磁场的旋转轴对称非理想气体中冲击波传播的相似解。使用等温和绝热流的李群分析讨论了相似解的所有可能情况。局部李群的生成器中涉及的任意常数带来了具有指数律和幂律冲击路径的各种可能的解决方案情况。详细讨论了等温和绝热流与幂律冲击路径的相似解。环境介质的密度被认为是恒定的。假定环境介质中的轴向和方位角的流体速度和磁场根据幂定律而变化。研究了Alfven Mach数，气体的绝热指数，非理想参数，旋转参数和初始磁场变化指数对冲击波强度和流量变量的影响。发现这些参数对冲击波具有衰减作用。还对等温和绝热流动情况下的所得结果进行了比较。